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Non-Contradiction

 
 
joefromchicago
 
  1  
Reply Thu 18 Mar, 2004 09:49 am
Adrian: The example you linked is worth exploring in detail:
    1. The Law of Non-Contradiction says nothing can be both A and not-A. 2. Only men have penises. (By definition) 3. A hermaphrodite has a penis. 4. Therefore, a hermaphrodite is a man. 5. Only women have vaginas. (By definition) 6. A hermaphrodite has a vagina. 7. Therefore, a hermaphrodite is a woman. 8. A woman is not a man. (By definition) 9. Therefore, a hermaphrodite is not a man. 10. Therefore, a hermaphrodite is both a man and not a man. 11. Therefore, a hermaphrodite is a counter-example to the Law of Non-Contradiction. 12. Therefore, the Law of Non-Contradiction is not true.

For paradoxes such as this, there is either something wrong with the rule or something wrong with the definitions.

The easiest way to refute this is to look at the definitions (steps 2 and 5). For instance, step 2 says: "only men have penises," which would equate to "for anything x, if x has a penis, then x is a man." Yet step 3 directly contradicts step 2 ("A hermaphrodite has a penis"), since we know, by definition, that a "hermaphrodite" has the sexual characteristics of both a man and a woman (assuming, arguendo, that true hermaphrodites actually exist). Thus there is something wrong with the definition in step 2.

The conclusion in step 12, then, is only true if we disregard the fact that it is based on flawed premises; i.e. there is an internal contradiction between the definitions in steps 2 and 5 and the fact statements in steps 3 and 6.

A simple tweaking of the definitions can solve the paradox. A revised step 2 would then read: "for anything x, if x has only male sex organs, then x is a man." In that event, the hermaphrodite would be neither a man nor a woman: that doesn't violate the law of non-contradiction, but it does give us a case of a tertium quid which contradicts the law of the excluded middle ("something is either A or not-A").
0 Replies
 
joefromchicago
 
  1  
Reply Thu 18 Mar, 2004 09:56 am
Re: truth
JLNobody wrote:
Joe, you ask if a process is a thing; my answer may not be satisfying, but here it is: All things are really processes. I am talking about a hypothetical man which you apparently see as a (hypothetical) thing (qua entity) and I am describing him as process. Just a matter of perspective.

You're right, JLN: your answer is not satisfying. But let me inquire further to see if we can arrive at a point of mutual satisfaction.

If all things are processes, and processes are constantly subject to change, can we say anything true about processes at all? In other words, if a man is both alive and dead (because parts of him are constantly dying or living), then how can we say anything about that man that is true for more than a split second?
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JLNobody
 
  1  
Reply Thu 18 Mar, 2004 10:43 am
truth
Joe, you are becoming a Taoist or zennist. That's precisely the question: how can we say anything about a Reality that is, as its fundamental nature, always changing? Well, we pretend that it is not changing. We turn verbs into nouns. It's a bit like turning running water into ice cubes so that we can catch it in our net. All of our utterances refer to fictively static "things" which are in actuality ever-changing processes. Taoists and zennists, when asked to describe the REALITY of something, generally remain silent or present gestures that SHOW process rather than talking ABOUT it.
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fresco
 
  1  
Reply Thu 18 Mar, 2004 11:05 am
...as they say in Yorkshire "Your're doing a grand job there JLN lad!".... :wink:
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Relative
 
  1  
Reply Thu 18 Mar, 2004 12:08 pm
Joe wrote:

Quote:
.. In that event, the hermaphrodite would be neither a man nor a woman: that doesn't violate the law of non-contradiction, but it does give us a case of a tertium quid which contradicts the law of the excluded middle ("something is either A or not-A").


If I may observe that this is not necessarily the case here: this would be if a woman was defined as 'not a man'. If defined as 'having female sexual organs' then it's not a problem-
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twyvel
 
  1  
Reply Thu 18 Mar, 2004 12:43 pm
jonny wrote:

Quote:
I agree with joefromshicago. Perhaps you have shown that I am both a tangible and intangible thing, but this doesn't violate the law of non-contradiction unless you also show that having the property of being intangible is merely the lack of having the property of being tangible. Otherwise you have only shown that I have contrary properties, like being good and being bad, but not contradictory properties. Perhaps we can clear up the discussion by more precicely stating the law of non-contradiction. I offer:

For any object, x, and any property, A, x cannot both have A and not have A.
Quote:
On a side note, there seems to be something paradoxical about saying of any object that it has the property of being non-objectified since if this was the case we couldn't ascribe properties to it at all because we can only ascribe properties to objects. (I might be missing something or confused on this point).
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twyvel
 
  1  
Reply Thu 18 Mar, 2004 12:45 pm
joefromchicago wrote:

Quote:
Your response does not "contradict my premise or my non-contradiction," it merely denies the possibility of contradiction (without, however, providing any evidence for that conclusion).

Jonny, then, is correct: you haven't offered any contradictories. I would, however, go further and say that you haven't even offered contraries. Your response is the equivalent of saying: "A thing can be simultaneously both 'A' and 'not-A,' where 'A' is defined as 'black' and 'not-A' is defined as 'tall.'"


No.

Dualistically speaking, You/I are simultaneously both objectification as body/ego and non-objectification as awareness.
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twyvel
 
  1  
Reply Thu 18 Mar, 2004 12:47 pm
joefromchicago wrote:

Quote:
What we can't assert, however, is that the contradictories "poinsettias are bad for cats to eat" and "poinsettias are good for cats to eat" are simultaneously true.
0 Replies
 
joefromchicago
 
  1  
Reply Thu 18 Mar, 2004 01:42 pm
Re: truth
JLNobody wrote:
Joe, you are becoming a Taoist or zennist.

I hope they have a pill for that.

JLNobody wrote:
That's precisely the question: how can we say anything about a Reality that is, as its fundamental nature, always changing?

Well, I think we agree that this is a consequence of your position. I just think that we have a fundamental disagreement over the desirability of that situation.

JLNobody wrote:
Well, we pretend that it is not changing. We turn verbs into nouns. It's a bit like turning running water into ice cubes so that we can catch it in our net. All of our utterances refer to fictively static "things" which are in actuality ever-changing processes.

Of course, if all our statements refer to fictively static "things," then our statements regarding "processes" are similiarly fictive. And since we can no more say anything true about "processes" than we can about "things," then we cannot say that "things" are actually "processes."

JLNobody wrote:
Taoists and zennists, when asked to describe the REALITY of something, generally remain silent or present gestures that SHOW process rather than talking ABOUT it.

I too have a gesture that demonstrates my opinion of the Taoist/Zennist position.
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joefromchicago
 
  1  
Reply Thu 18 Mar, 2004 01:44 pm
twyvel wrote:
No.

Dualistically speaking, You/I are simultaneously both objectification as body/ego and non-objectification as awareness.

How do you know that?
0 Replies
 
fresco
 
  1  
Reply Thu 18 Mar, 2004 03:08 pm
Seems to me that the concepts of "thing" and "truth" are tautologically linked. i.e. The "truth" of statement "the thing X has property A" implies continuity of X long enough for A to "be observed". But as JLN has pointed out, both "thingness" and "observation" are transitory processes, and "truth" is no more related to "reality" than a snapshot is to the flux of existence.

The law of "non-contradiction" although "mathematically" correct is based on such petrified snapshots, and note also that even the "simultaneity" on which it depends is (after Einstein) "observer dependent".

As stated previously. what we have here is a discussion of the applicability of "bi-valent logic". Like all derrivatives of more general semantics such applicability will be limited. The temptation/mistake is try to make "reality" conform to a particular system as though this were a final arbiter of "coherence".
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jonny
 
  1  
Reply Thu 18 Mar, 2004 03:48 pm
twyvel-

So let me get this straight. There is an 'I' that is objectified/observed, meaning that it is the subject of my thoughts about myself, and there is an 'I' that is non-objectified/non-observed, meaning that it is pure awareness which actually has the thoughts. Therefore I have the properties of being both objectified and non-objectified which is a counterexample to the law of non-contradiction.

I think you are equivocating on the word 'I'. The objectified/observed 'I' is merely the object of thought to which I ascribe all the properties that I think I have, like being in my bedroom, being male, etc. The non-objectified/non-observed 'I' is a completely different object to which I cannot ascribe any properties because it's the object that does the ascribing. In other words, the observer observes something which it calls 'I' though this cannot be the observer since you maintain that awareness cannot be aware of itself (twyvel: the non-objectified subject cannot be observed).

The only way out I see is to maintain that it is the non-observed 'I' is in fact the object that actually has the properties. There are two problems with this fix: 1) there is no reason to believe this over the law of non-contradiction, and 2) the price is way to high - for we would lose any and all certain knowledge about ourselves since we could not actually observe ourselves.
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JLNobody
 
  1  
Reply Thu 18 Mar, 2004 03:49 pm
truth
That was an even grander job, Fresco Ladi. Very Happy
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jonny
 
  1  
Reply Thu 18 Mar, 2004 04:09 pm
Since we are dealing with logic, lets see if a logically constructed object can act as a counterexample:

Some definitions:
(i) let a =df. an object that has no properties.
(ii) let A =df. has properties.
(iii) let B =df. is an object.

One premise:
(I) For all x, if x has B then x has A.

The proof:
1. a has B. (from i and iii)
2. Therefore a has A. (from 1 and I)
3. a does not have A. (from i and ii)
4. Therefore a has A. and a does not have A. (from 2 and 3)
5. Therefore a violates the law of non-contradiction.

Hokey - yes. Mindless wordplay - yes. But it is a counterexample to the law of non-contradiction.
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fresco
 
  1  
Reply Thu 18 Mar, 2004 04:33 pm
jonny

Yes...a central issue which arises from such "wordplay" is an analysis of the concept of "objectivity" in particular, and of course the more general issues of "reality" and the limits of language.
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Relative
 
  1  
Reply Thu 18 Mar, 2004 04:34 pm
jonny : this is just another disguise of a liar paradox.
(i) states x has no properties
(iii) states x has a property (of being an object)

This is a contradiction in definitions, nothing more.
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fresco
 
  1  
Reply Thu 18 Mar, 2004 05:30 pm
Consider the textual message:

T/-\E C/-\T

In what way is the symbol /-\ "an object"?

1. I draw it to your attention (property=FOCUS)
2. It can function as either an E or A (property=AMBIGUITY)

So I far I assume we can agree on the "truth" of 1. and 2.

But instead of the above, consider instead the symbol /-\ on its own

Now we might only agree on the "truth" of property 1.

I am making the points
(a) that "properties" (set memberships) are relative to purposes of the observer, or specific observational contextual totalities.
(b) that "objectivity" itself implies a minimum of property 1. which itself is observer and context related.
(c) "truth" is negotiable.

This scenario of "ambiguity" synthetically highlights these points. In the flux of existence ambiguities (like contradictions) scarcely arise.
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twyvel
 
  1  
Reply Thu 18 Mar, 2004 08:04 pm
joefromchicago



Quote:


Dualistically speaking, You/I are simultaneously both objectification as body/ego and non-objectification as awareness.

Quote:
How do you know that?




I know it though intuition, observation, reason, contemplation etc.

note: by 'objectification' I don't mean to suggest the existence of autonomous objects but only what appears to be such. As JLNobody and fresco have said, observation is a process, an action in which a supposed observer and a supposed observed are actually in continuous flux.

And as regards contradictions, for someone to claim that they can observe the awareness that they are is a contradiction.
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twyvel
 
  1  
Reply Thu 18 Mar, 2004 08:10 pm
jonny



Quote:
The only way out I see is to maintain that it is the non-observed 'I' is in fact the object that actually has the properties. There are two problems with this fix: 1) there is no reason to believe this over the law of non-contradiction, and 2) the price is way to high - for we would lose any and all certain knowledge about ourselves since we could not actually observe ourselves.




That's correct, awareness cannot be observed, the unobservable observer is a blind spot in observation. As such what we take to be our 'self' as body-thoughts-ego is in fact an object not a subject, and in as much as it is considered a subject it is a pseudo subject. There is in this sense no self.

Who we are as awareness is unknown because it cannot be made an object of observation without ceasing to be what it(?) is, and there is nothing for it to be known by, i.e. objects don't know anything.
0 Replies
 
joefromchicago
 
  1  
Reply Thu 18 Mar, 2004 09:06 pm
twyvel wrote:
Re: generalization

Like most or all objects (things), poinsettias and cats are a composite of many elements. Some of what makes up a poinsettia, such as vitamins, might be good for the cats liver etc. and yet other elements may be bad for other organs or parts of the cats body, or the cats psychological well being, etc.

It is like saying, "This >group of hundreds of objects/elements< (the poinsettias) cannot simultaneously be both bad and good for this >group of hundreds of objects/elements< (the cat) Which is false for there is bound to be some objects/substances/elements of the poinsettias that are good and some that are bad (at one and the same time) for the many things/events that constitute a cat. We don't know.

These are merely empirical objections.

twyvel wrote:
Secondly, there are hundreds of varieties of pointsettias and hundreds of varieties of cats, both domestic and wild, of which, depending of the variety some may possess some elements that others do not.

There is also gender and age considerations as well. Point is, the more general your generlization is the less it says.You have to be more specific.

As are these.

twyvel wrote:
And the question may become an issue of 'purity', i.e. is there any such thing?..etc.

And so is that.
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